Beyond that, I would say that you should try a bit harder to learn about the delta function without just asking us to explain it. It is typically introduced in either a Quantum mechanics course or an Electromagnetism course. Griffiths text on both subjects gives a non rigorous intro to the delta function.

So are you familiar with the 1-dimensional Dirac delta function? If so, the 3-dimensional delta function is just the product of three 1-dimensional delta functions, one for each component of the vector ##\vec{r}##: